Download
CT Impulse Presentation Transcript:
1.EEE223 Signals & Systems
2.Outline
CT Impulse (continued)
Systems
With and without memory
Invertible and inverse systems
Causal systems
Stable systems
Time invariant systems
Linear systems
3.CT unit impulse
Sampling property:
4.CT unit impulse
Derivatives of CT signals:
5.Systems
Transform input signals to output signals
OR
Input signals cause systems to respond in certain ways resulting in other output signals
6.Interconnections of systems
Series or cascade
Parallel
Series – parallel
Feedback interconnections
7.Properties: Memory
Without memory: Output ONLY depends on input at the same time, e.g.
y(t) = 2x(t) + x2(t)
With memory:
8.Properties: Memory
Simple delay: (memory)
y[n] = x[n-2]
Accumulator
What if output depends on FUTURE values?
9.Properties: Invertibility
Distinct inputs lead to distinct outputs (observe output, deduce input)
Then inverse systems possible
Encoding – decoding
Modulation – demodulation
10.Properties: Invertibility
11.Properties: Causality
Output depends only on present and past values of input
y[n] = x[n] + x[n-1] Causal
y(t) = x(t+1) Non-causal
Memoryless systems are causal
What about y[n] = x[-n] ?
12.Properties: Stability
Bounded input leads to bounded output
y[n] = 1.05 y[n-1] + x[n] ????
y[n] = nx[n] ???
tx(t)?? ex(t) ??
Find counterexamples for instability
13.Properties: Time Invariance
Time shift in input leads to identical time shift in the output
x[n-no] -> y[n-no]
Or
x(t-to) -> y(t-to)
14.Properties: Time Invariance
y[n] = nx[n]??
y(t) = Cos(x(t))
15.Obeys principle of superposition
Additivity
x1 + x2 -> y1 + y2
Homogeneity
ax -> ay
